Show that : (i) tan 48 tan 23 tan 42 tan 67 = 1 (ii) cos 38 cos 52 – sin 38 sin 52 = 0

Solution :

(i)  L.H.S = tan 48 tan 23 tan 42 tan 67 = \(1\over cot 48\). tan 23 tan 42 \(1\over cot 67\)

= \(1\over cot (90 – 42)\). tan 23 tan 42 \(1\over cot (90 – 23)\) = \(1\over tan 42\). tan 23 tan 42 \(1\over tan 23\)

= 1 = R.H.S.

(ii)  L.H.S = cos 38 cos 52 – sin 38 sin 52 = cos 38.cos(90 – 38) – sin 38 sin(90 – 38)

= cos 38 sin 38 – sin 38 cos 38 = 0 = R.H.S.

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